TSTP Solution File: SEU388+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU388+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:16:01 EDT 2022
% Result : Unknown 3.01s 3.18s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU388+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 08:03:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.80/3.00 ----- Otter 3.3f, August 2004 -----
% 2.80/3.00 The process was started by sandbox on n022.cluster.edu,
% 2.80/3.00 Wed Jul 27 08:03:50 2022
% 2.80/3.00 The command was "./otter". The process ID is 26368.
% 2.80/3.00
% 2.80/3.00 set(prolog_style_variables).
% 2.80/3.00 set(auto).
% 2.80/3.00 dependent: set(auto1).
% 2.80/3.00 dependent: set(process_input).
% 2.80/3.00 dependent: clear(print_kept).
% 2.80/3.00 dependent: clear(print_new_demod).
% 2.80/3.00 dependent: clear(print_back_demod).
% 2.80/3.00 dependent: clear(print_back_sub).
% 2.80/3.00 dependent: set(control_memory).
% 2.80/3.00 dependent: assign(max_mem, 12000).
% 2.80/3.00 dependent: assign(pick_given_ratio, 4).
% 2.80/3.00 dependent: assign(stats_level, 1).
% 2.80/3.00 dependent: assign(max_seconds, 10800).
% 2.80/3.00 clear(print_given).
% 2.80/3.00
% 2.80/3.00 formula_list(usable).
% 2.80/3.00 all A (A=A).
% 2.80/3.00 all A (rel_str(A)-> (strict_rel_str(A)->A=rel_str_of(the_carrier(A),the_InternalRel(A)))).
% 2.80/3.00 all A B (in(A,B)-> -in(B,A)).
% 2.80/3.00 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&up_complete_relstr(A)&join_complete_relstr(A))).
% 2.80/3.00 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&join_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&lower_bounded_relstr(A))).
% 2.80/3.00 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&lower_bounded_relstr(A)&up_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A))).
% 2.80/3.00 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&antisymmetric_relstr(A)&join_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&antisymmetric_relstr(A)&with_infima_relstr(A))).
% 2.80/3.00 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&antisymmetric_relstr(A)&upper_bounded_relstr(A)&join_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&upper_bounded_relstr(A))).
% 2.80/3.00 all A (empty(A)->finite(A)).
% 2.80/3.00 all A (rel_str(A)-> (with_suprema_relstr(A)-> -empty_carrier(A))).
% 2.80/3.00 all A (empty(A)->relation(A)).
% 2.80/3.00 all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 2.80/3.00 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (empty(B)->open_subset(B,A)&closed_subset(B,A))))).
% 2.80/3.00 all A (rel_str(A)-> (-empty_carrier(A)&complete_relstr(A)-> -empty_carrier(A)&with_suprema_relstr(A)&with_infima_relstr(A))).
% 2.80/3.00 all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 2.80/3.00 all A (rel_str(A)-> (with_infima_relstr(A)-> -empty_carrier(A))).
% 2.80/3.00 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (empty(B)->boundary_set(B,A))))).
% 2.80/3.00 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&trivial_carrier(A)-> -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&complete_relstr(A))).
% 2.80/3.00 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (empty(B)->nowhere_dense(B,A))))).
% 2.80/3.00 all A (rel_str(A)-> (-empty_carrier(A)&complete_relstr(A)-> -empty_carrier(A)&bounded_relstr(A))).
% 2.80/3.00 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (nowhere_dense(B,A)->boundary_set(B,A))))).
% 2.80/3.00 all A (rel_str(A)-> (bounded_relstr(A)->lower_bounded_relstr(A)&upper_bounded_relstr(A))).
% 2.80/3.00 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)&boundary_set(B,A)->boundary_set(B,A)&nowhere_dense(B,A))))).
% 2.80/3.00 all A (rel_str(A)-> (-empty_carrier(A)&reflexive_relstr(A)&trivial_carrier(A)-> -empty_carrier(A)&reflexive_relstr(A)&connected_relstr(A))).
% 2.80/3.00 all A (rel_str(A)-> (lower_bounded_relstr(A)&upper_bounded_relstr(A)->bounded_relstr(A))).
% 2.80/3.00 all A (topological_space(A)&top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (open_subset(B,A)&nowhere_dense(B,A)->empty(B)&open_subset(B,A)&closed_subset(B,A)&v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)&boundary_set(B,A)&nowhere_dense(B,A))))).
% 2.80/3.00 all A (rel_str(A)-> (reflexive_relstr(A)&with_suprema_relstr(A)&up_complete_relstr(A)-> -empty_carrier(A)&reflexive_relstr(A)&with_suprema_relstr(A)&upper_bounded_relstr(A))).
% 2.80/3.00 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,the_carrier(A))->neighborhood_system(A,B)=a_2_0_yellow19(A,B)))).
% 2.80/3.00 all A B (relation_of2(B,A,A)->strict_rel_str(rel_str_of(A,B))&rel_str(rel_str_of(A,B))).
% 2.80/3.00 $T.
% 2.80/3.00 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)&element(B,the_carrier(A))->element(neighborhood_system(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A)))))).
% 2.80/3.00 $T.
% 2.80/3.00 all A (one_sorted_str(A)->element(cast_as_carrier_subset(A),powerset(the_carrier(A)))).
% 2.80/3.00 $T.
% 2.80/3.00 all A (strict_rel_str(boole_POSet(A))&rel_str(boole_POSet(A))).
% 2.80/3.00 all A (rel_str(A)->one_sorted_str(A)).
% 2.80/3.00 all A (top_str(A)->one_sorted_str(A)).
% 2.80/3.00 $T.
% 2.80/3.00 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)&element(B,the_carrier(A))-> (all C (point_neighbourhood(C,A,B)->element(C,powerset(the_carrier(A)))))).
% 2.80/3.00 $T.
% 2.80/3.00 $T.
% 2.80/3.00 all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 2.80/3.00 all A (rel_str(A)->relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))).
% 2.80/3.00 $T.
% 2.80/3.00 exists A rel_str(A).
% 2.80/3.00 exists A top_str(A).
% 2.80/3.00 exists A one_sorted_str(A).
% 2.80/3.00 all A B (-empty_carrier(A)&topological_space(A)&top_str(A)&element(B,the_carrier(A))-> (exists C point_neighbourhood(C,A,B))).
% 2.80/3.00 all A B exists C relation_of2(C,A,B).
% 2.80/3.00 all A exists B element(B,A).
% 2.80/3.00 all A B exists C relation_of2_as_subset(C,A,B).
% 2.80/3.00 empty(empty_set).
% 2.80/3.00 relation(empty_set).
% 2.80/3.00 relation_empty_yielding(empty_set).
% 2.80/3.00 all A B (finite(A)&finite(B)->finite(cartesian_product2(A,B))).
% 2.80/3.00 all A (-empty_carrier(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&lower_relstr_subset(cast_as_carrier_subset(A),A)&upper_relstr_subset(cast_as_carrier_subset(A),A)).
% 2.80/3.00 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(the_carrier(A))).
% 2.80/3.00 all A (-empty(powerset(A))).
% 2.80/3.00 all A (-empty_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))&lower_bounded_relstr(boole_POSet(A))&upper_bounded_relstr(boole_POSet(A))&bounded_relstr(boole_POSet(A))&up_complete_relstr(boole_POSet(A))&join_complete_relstr(boole_POSet(A))& -v1_yellow_3(boole_POSet(A))&distributive_relstr(boole_POSet(A))&heyting_relstr(boole_POSet(A))&complemented_relstr(boole_POSet(A))&boolean_relstr(boole_POSet(A))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_relstr(boole_POSet(A))).
% 2.80/3.00 all A (-empty_carrier(A)&one_sorted_str(A)-> -empty(cast_as_carrier_subset(A))).
% 2.80/3.00 all A (with_suprema_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&directed_subset(cast_as_carrier_subset(A),A)).
% 2.80/3.00 all A (-empty(A)-> -empty_carrier(boole_POSet(A))& -trivial_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))&lower_bounded_relstr(boole_POSet(A))&upper_bounded_relstr(boole_POSet(A))&bounded_relstr(boole_POSet(A))&up_complete_relstr(boole_POSet(A))&join_complete_relstr(boole_POSet(A))& -v1_yellow_3(boole_POSet(A))&distributive_relstr(boole_POSet(A))&heyting_relstr(boole_POSet(A))&complemented_relstr(boole_POSet(A))&boolean_relstr(boole_POSet(A))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_relstr(boole_POSet(A))).
% 2.80/3.00 all A (-empty_carrier(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))).
% 2.80/3.00 all A (-empty_carrier(A)&upper_bounded_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&directed_subset(cast_as_carrier_subset(A),A)).
% 2.80/3.00 empty(empty_set).
% 2.80/3.00 relation(empty_set).
% 2.80/3.00 all A B (-empty(A)& -empty(B)-> -empty(cartesian_product2(A,B))).
% 2.80/3.00 all A (with_infima_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&filtered_subset(cast_as_carrier_subset(A),A)).
% 2.80/3.00 all A (topological_space(A)&top_str(A)->closed_subset(cast_as_carrier_subset(A),A)).
% 2.80/3.00 all A (-empty_carrier(A)&lower_bounded_relstr(A)&rel_str(A)-> -empty(cast_as_carrier_subset(A))&filtered_subset(cast_as_carrier_subset(A),A)).
% 2.80/3.00 all A (-empty_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))).
% 2.86/3.00 all A (topological_space(A)&top_str(A)->open_subset(cast_as_carrier_subset(A),A)&closed_subset(cast_as_carrier_subset(A),A)).
% 2.86/3.00 all A (-empty_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))&lower_bounded_relstr(boole_POSet(A))&upper_bounded_relstr(boole_POSet(A))&bounded_relstr(boole_POSet(A))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_relstr(boole_POSet(A))).
% 2.86/3.00 all A (-empty_carrier(boole_POSet(A))&strict_rel_str(boole_POSet(A))&reflexive_relstr(boole_POSet(A))&transitive_relstr(boole_POSet(A))&antisymmetric_relstr(boole_POSet(A))&lower_bounded_relstr(boole_POSet(A))&upper_bounded_relstr(boole_POSet(A))&bounded_relstr(boole_POSet(A))&directed_relstr(boole_POSet(A))&up_complete_relstr(boole_POSet(A))&join_complete_relstr(boole_POSet(A))& -v1_yellow_3(boole_POSet(A))&with_suprema_relstr(boole_POSet(A))&with_infima_relstr(boole_POSet(A))&complete_relstr(boole_POSet(A))).
% 2.86/3.00 all A (top_str(A)->dense(cast_as_carrier_subset(A),A)).
% 2.86/3.00 all A B C (-empty_carrier(B)&topological_space(B)&top_str(B)&element(C,the_carrier(B))-> (in(A,a_2_0_yellow19(B,C))<-> (exists D (point_neighbourhood(D,B,C)&A=D)))).
% 2.86/3.00 all A B (relation_of2(B,A,A)-> (all C D (rel_str_of(A,B)=rel_str_of(C,D)->A=C&B=D))).
% 2.86/3.00 all A (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&filtered_subset(B,A)&upper_relstr_subset(B,A)))).
% 2.86/3.00 all A (reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&directed_subset(B,A)&filtered_subset(B,A)&lower_relstr_subset(B,A)&upper_relstr_subset(B,A)))).
% 2.86/3.00 exists A (rel_str(A)& -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&connected_relstr(A)).
% 2.86/3.00 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)&up_complete_relstr(A)&join_complete_relstr(A)).
% 2.86/3.00 exists A (-empty(A)&finite(A)).
% 2.86/3.00 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&complete_relstr(A)).
% 2.86/3.00 exists A (empty(A)&relation(A)).
% 2.86/3.00 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 2.86/3.00 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&open_subset(B,A)))).
% 2.86/3.00 all A (rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&directed_subset(B,A)&filtered_subset(B,A)))).
% 2.86/3.00 exists A (rel_str(A)& -empty_carrier(A)& -trivial_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)& -v1_yellow_3(A)&distributive_relstr(A)&heyting_relstr(A)&complemented_relstr(A)&boolean_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)).
% 2.86/3.00 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)&trivial_carrier(A)).
% 2.86/3.00 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)).
% 2.86/3.00 exists A (-empty(A)&relation(A)).
% 2.86/3.00 all A exists B (element(B,powerset(A))&empty(B)).
% 2.86/3.00 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&open_subset(B,A)&closed_subset(B,A)))).
% 2.86/3.00 all A (-empty_carrier(A)&reflexive_relstr(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&finite(B)&directed_subset(B,A)&filtered_subset(B,A)))).
% 2.86/3.00 all A exists B (element(B,powerset(powerset(A)))& -empty(B)&finite(B)).
% 2.86/3.00 exists A (rel_str(A)& -empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&antisymmetric_relstr(A)&with_suprema_relstr(A)&with_infima_relstr(A)&complete_relstr(A)&lower_bounded_relstr(A)&upper_bounded_relstr(A)&bounded_relstr(A)).
% 2.86/3.00 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.86/3.00 exists A (relation(A)&relation_empty_yielding(A)).
% 2.86/3.00 exists A (one_sorted_str(A)& -empty_carrier(A)).
% 2.86/3.00 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&open_subset(B,A)&closed_subset(B,A)))).
% 2.86/3.00 all A (one_sorted_str(A)-> (exists B (element(B,powerset(powerset(the_carrier(A))))& -empty(B)&finite(B)))).
% 2.86/3.00 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 2.86/3.00 all A (top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&empty(B)&v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)&boundary_set(B,A)))).
% 2.86/3.00 exists A (rel_str(A)& -empty_carrier(A)&strict_rel_str(A)&transitive_relstr(A)&directed_relstr(A)).
% 2.86/3.00 all A (-empty_carrier(A)&one_sorted_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)))).
% 2.86/3.00 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&empty(B)&open_subset(B,A)&closed_subset(B,A)&v1_membered(B)&v2_membered(B)&v3_membered(B)&v4_membered(B)&v5_membered(B)&boundary_set(B,A)&nowhere_dense(B,A)))).
% 2.86/3.00 all A (topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&closed_subset(B,A)))).
% 2.86/3.00 all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&closed_subset(B,A)))).
% 2.86/3.00 all A (rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))&lower_relstr_subset(B,A)&upper_relstr_subset(B,A)))).
% 2.86/3.00 all A (-empty_carrier(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&lower_relstr_subset(B,A)&upper_relstr_subset(B,A)))).
% 2.86/3.00 all A (-empty_carrier(A)&reflexive_relstr(A)&transitive_relstr(A)&rel_str(A)-> (exists B (element(B,powerset(the_carrier(A)))& -empty(B)&directed_subset(B,A)&lower_relstr_subset(B,A)))).
% 2.86/3.00 all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 2.86/3.00 all A B subset(A,A).
% 2.86/3.00 all A B (in(A,B)->element(A,B)).
% 2.86/3.00 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.86/3.00 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 2.86/3.00 all A B (element(A,powerset(B))<->subset(A,B)).
% 2.86/3.00 -(all A (-empty_carrier(A)&topological_space(A)&top_str(A)-> (all B (element(B,the_carrier(A))-> (all C (in(C,neighborhood_system(A,B))<->point_neighbourhood(C,A,B))))))).
% 2.86/3.00 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 2.86/3.00 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 2.86/3.00 all A (empty(A)->A=empty_set).
% 2.86/3.00 all A B (-(in(A,B)&empty(B))).
% 2.86/3.00 all A B (-(empty(A)&A!=B&empty(B))).
% 2.86/3.00 end_of_list.
% 2.86/3.00
% 2.86/3.00 -------> usable clausifies to:
% 2.86/3.00
% 2.86/3.00 list(usable).
% 2.86/3.00 0 [] A=A.
% 2.86/3.00 0 [] -rel_str(A)| -strict_rel_str(A)|A=rel_str_of(the_carrier(A),the_InternalRel(A)).
% 2.86/3.00 0 [] -in(A,B)| -in(B,A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|up_complete_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|join_complete_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -join_complete_relstr(A)|lower_bounded_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|with_infima_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|complete_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|bounded_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -join_complete_relstr(A)|with_infima_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -join_complete_relstr(A)|with_suprema_relstr(A).
% 2.86/3.00 0 [] -empty(A)|finite(A).
% 2.86/3.00 0 [] -rel_str(A)| -with_suprema_relstr(A)| -empty_carrier(A).
% 2.86/3.00 0 [] -empty(A)|relation(A).
% 2.86/3.00 0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|open_subset(B,A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|closed_subset(B,A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_suprema_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_infima_relstr(A).
% 2.86/3.00 0 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.86/3.00 0 [] -rel_str(A)| -with_infima_relstr(A)| -empty_carrier(A).
% 2.86/3.00 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|boundary_set(B,A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|transitive_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|antisymmetric_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|complete_relstr(A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|nowhere_dense(B,A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|bounded_relstr(A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -nowhere_dense(B,A)|boundary_set(B,A).
% 2.86/3.00 0 [] -rel_str(A)| -bounded_relstr(A)|lower_bounded_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)| -bounded_relstr(A)|upper_bounded_relstr(A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)| -boundary_set(B,A)|nowhere_dense(B,A).
% 2.86/3.00 0 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|connected_relstr(A).
% 2.86/3.00 0 [] -rel_str(A)| -lower_bounded_relstr(A)| -upper_bounded_relstr(A)|bounded_relstr(A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|empty(B).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|closed_subset(B,A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v1_membered(B).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v2_membered(B).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v3_membered(B).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v4_membered(B).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v5_membered(B).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|boundary_set(B,A).
% 2.86/3.00 0 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)| -empty_carrier(A).
% 2.86/3.00 0 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))|neighborhood_system(A,B)=a_2_0_yellow19(A,B).
% 2.86/3.00 0 [] -relation_of2(B,A,A)|strict_rel_str(rel_str_of(A,B)).
% 2.86/3.00 0 [] -relation_of2(B,A,A)|rel_str(rel_str_of(A,B)).
% 2.86/3.00 0 [] $T.
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))|element(neighborhood_system(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))).
% 2.86/3.00 0 [] $T.
% 2.86/3.00 0 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] $T.
% 2.86/3.00 0 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.00 0 [] rel_str(boole_POSet(A)).
% 2.86/3.00 0 [] -rel_str(A)|one_sorted_str(A).
% 2.86/3.00 0 [] -top_str(A)|one_sorted_str(A).
% 2.86/3.00 0 [] $T.
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -point_neighbourhood(C,A,B)|element(C,powerset(the_carrier(A))).
% 2.86/3.00 0 [] $T.
% 2.86/3.00 0 [] $T.
% 2.86/3.00 0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 2.86/3.00 0 [] -rel_str(A)|relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)).
% 2.86/3.00 0 [] $T.
% 2.86/3.00 0 [] rel_str($c1).
% 2.86/3.00 0 [] top_str($c2).
% 2.86/3.00 0 [] one_sorted_str($c3).
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))|point_neighbourhood($f1(A,B),A,B).
% 2.86/3.00 0 [] relation_of2($f2(A,B),A,B).
% 2.86/3.00 0 [] element($f3(A),A).
% 2.86/3.00 0 [] relation_of2_as_subset($f4(A,B),A,B).
% 2.86/3.00 0 [] empty(empty_set).
% 2.86/3.00 0 [] relation(empty_set).
% 2.86/3.00 0 [] relation_empty_yielding(empty_set).
% 2.86/3.00 0 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 2.86/3.00 0 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 2.86/3.00 0 [] -empty(powerset(A)).
% 2.86/3.00 0 [] -empty_carrier(boole_POSet(A)).
% 2.86/3.00 0 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.00 0 [] reflexive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] transitive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] lower_bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] upper_bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] up_complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] join_complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] -v1_yellow_3(boole_POSet(A)).
% 2.86/3.00 0 [] distributive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] heyting_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] complemented_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] boolean_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] with_suprema_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] with_infima_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.00 0 [] -with_suprema_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.00 0 [] -with_suprema_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] empty(A)| -empty_carrier(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)| -trivial_carrier(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|strict_rel_str(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|reflexive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|transitive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|lower_bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|upper_bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|up_complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|join_complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)| -v1_yellow_3(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|distributive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|heyting_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|complemented_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|boolean_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|with_suprema_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|with_infima_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty(A)|complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] empty(empty_set).
% 2.86/3.00 0 [] relation(empty_set).
% 2.86/3.00 0 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 2.86/3.00 0 [] -with_infima_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.00 0 [] -with_infima_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|closed_subset(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] -empty_carrier(boole_POSet(A)).
% 2.86/3.00 0 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.00 0 [] reflexive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] transitive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|open_subset(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|closed_subset(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] -empty_carrier(boole_POSet(A)).
% 2.86/3.00 0 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.00 0 [] reflexive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] transitive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] lower_bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] upper_bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] with_suprema_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] with_infima_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] -empty_carrier(boole_POSet(A)).
% 2.86/3.00 0 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.00 0 [] reflexive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] transitive_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] lower_bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] upper_bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] bounded_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] directed_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] up_complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] join_complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] -v1_yellow_3(boole_POSet(A)).
% 2.86/3.00 0 [] with_suprema_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] with_infima_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] complete_relstr(boole_POSet(A)).
% 2.86/3.00 0 [] -top_str(A)|dense(cast_as_carrier_subset(A),A).
% 2.86/3.00 0 [] empty_carrier(B)| -topological_space(B)| -top_str(B)| -element(C,the_carrier(B))| -in(A,a_2_0_yellow19(B,C))|point_neighbourhood($f5(A,B,C),B,C).
% 2.86/3.00 0 [] empty_carrier(B)| -topological_space(B)| -top_str(B)| -element(C,the_carrier(B))| -in(A,a_2_0_yellow19(B,C))|A=$f5(A,B,C).
% 2.86/3.00 0 [] empty_carrier(B)| -topological_space(B)| -top_str(B)| -element(C,the_carrier(B))|in(A,a_2_0_yellow19(B,C))| -point_neighbourhood(D,B,C)|A!=D.
% 2.86/3.00 0 [] -relation_of2(B,A,A)|rel_str_of(A,B)!=rel_str_of(C,D)|A=C.
% 2.86/3.00 0 [] -relation_of2(B,A,A)|rel_str_of(A,B)!=rel_str_of(C,D)|B=D.
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f6(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f6(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|filtered_subset($f6(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|upper_relstr_subset($f6(A),A).
% 2.86/3.00 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|element($f7(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)| -empty($f7(A)).
% 2.86/3.00 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|directed_subset($f7(A),A).
% 2.86/3.00 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|filtered_subset($f7(A),A).
% 2.86/3.00 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|lower_relstr_subset($f7(A),A).
% 2.86/3.00 0 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|upper_relstr_subset($f7(A),A).
% 2.86/3.00 0 [] rel_str($c4).
% 2.86/3.00 0 [] -empty_carrier($c4).
% 2.86/3.00 0 [] reflexive_relstr($c4).
% 2.86/3.00 0 [] transitive_relstr($c4).
% 2.86/3.00 0 [] antisymmetric_relstr($c4).
% 2.86/3.00 0 [] connected_relstr($c4).
% 2.86/3.00 0 [] rel_str($c5).
% 2.86/3.00 0 [] -empty_carrier($c5).
% 2.86/3.00 0 [] strict_rel_str($c5).
% 2.86/3.00 0 [] reflexive_relstr($c5).
% 2.86/3.00 0 [] transitive_relstr($c5).
% 2.86/3.00 0 [] antisymmetric_relstr($c5).
% 2.86/3.00 0 [] with_suprema_relstr($c5).
% 2.86/3.00 0 [] with_infima_relstr($c5).
% 2.86/3.00 0 [] complete_relstr($c5).
% 2.86/3.00 0 [] lower_bounded_relstr($c5).
% 2.86/3.00 0 [] upper_bounded_relstr($c5).
% 2.86/3.00 0 [] bounded_relstr($c5).
% 2.86/3.00 0 [] up_complete_relstr($c5).
% 2.86/3.00 0 [] join_complete_relstr($c5).
% 2.86/3.00 0 [] -empty($c6).
% 2.86/3.00 0 [] finite($c6).
% 2.86/3.00 0 [] rel_str($c7).
% 2.86/3.00 0 [] -empty_carrier($c7).
% 2.86/3.00 0 [] strict_rel_str($c7).
% 2.86/3.00 0 [] reflexive_relstr($c7).
% 2.86/3.00 0 [] transitive_relstr($c7).
% 2.86/3.00 0 [] antisymmetric_relstr($c7).
% 2.86/3.00 0 [] complete_relstr($c7).
% 2.86/3.00 0 [] empty($c8).
% 2.86/3.00 0 [] relation($c8).
% 2.86/3.00 0 [] empty(A)|element($f8(A),powerset(A)).
% 2.86/3.00 0 [] empty(A)| -empty($f8(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|element($f9(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|open_subset($f9(A),A).
% 2.86/3.00 0 [] -rel_str(A)|element($f10(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] -rel_str(A)|directed_subset($f10(A),A).
% 2.86/3.00 0 [] -rel_str(A)|filtered_subset($f10(A),A).
% 2.86/3.00 0 [] rel_str($c9).
% 2.86/3.00 0 [] -empty_carrier($c9).
% 2.86/3.00 0 [] -trivial_carrier($c9).
% 2.86/3.00 0 [] strict_rel_str($c9).
% 2.86/3.00 0 [] reflexive_relstr($c9).
% 2.86/3.00 0 [] transitive_relstr($c9).
% 2.86/3.00 0 [] antisymmetric_relstr($c9).
% 2.86/3.00 0 [] lower_bounded_relstr($c9).
% 2.86/3.00 0 [] upper_bounded_relstr($c9).
% 2.86/3.00 0 [] bounded_relstr($c9).
% 2.86/3.00 0 [] -v1_yellow_3($c9).
% 2.86/3.00 0 [] distributive_relstr($c9).
% 2.86/3.00 0 [] heyting_relstr($c9).
% 2.86/3.00 0 [] complemented_relstr($c9).
% 2.86/3.00 0 [] boolean_relstr($c9).
% 2.86/3.00 0 [] with_suprema_relstr($c9).
% 2.86/3.00 0 [] with_infima_relstr($c9).
% 2.86/3.00 0 [] rel_str($c10).
% 2.86/3.00 0 [] -empty_carrier($c10).
% 2.86/3.00 0 [] strict_rel_str($c10).
% 2.86/3.00 0 [] reflexive_relstr($c10).
% 2.86/3.00 0 [] transitive_relstr($c10).
% 2.86/3.00 0 [] antisymmetric_relstr($c10).
% 2.86/3.00 0 [] with_suprema_relstr($c10).
% 2.86/3.00 0 [] with_infima_relstr($c10).
% 2.86/3.00 0 [] complete_relstr($c10).
% 2.86/3.00 0 [] trivial_carrier($c10).
% 2.86/3.00 0 [] rel_str($c11).
% 2.86/3.00 0 [] -empty_carrier($c11).
% 2.86/3.00 0 [] strict_rel_str($c11).
% 2.86/3.00 0 [] reflexive_relstr($c11).
% 2.86/3.00 0 [] transitive_relstr($c11).
% 2.86/3.00 0 [] antisymmetric_relstr($c11).
% 2.86/3.00 0 [] with_suprema_relstr($c11).
% 2.86/3.00 0 [] with_infima_relstr($c11).
% 2.86/3.00 0 [] complete_relstr($c11).
% 2.86/3.00 0 [] -empty($c12).
% 2.86/3.00 0 [] relation($c12).
% 2.86/3.00 0 [] element($f11(A),powerset(A)).
% 2.86/3.00 0 [] empty($f11(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|element($f12(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|open_subset($f12(A),A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|closed_subset($f12(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|element($f13(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -empty($f13(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|finite($f13(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|directed_subset($f13(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|filtered_subset($f13(A),A).
% 2.86/3.00 0 [] element($f14(A),powerset(powerset(A))).
% 2.86/3.00 0 [] -empty($f14(A)).
% 2.86/3.00 0 [] finite($f14(A)).
% 2.86/3.00 0 [] rel_str($c13).
% 2.86/3.00 0 [] -empty_carrier($c13).
% 2.86/3.00 0 [] reflexive_relstr($c13).
% 2.86/3.00 0 [] transitive_relstr($c13).
% 2.86/3.00 0 [] antisymmetric_relstr($c13).
% 2.86/3.00 0 [] with_suprema_relstr($c13).
% 2.86/3.00 0 [] with_infima_relstr($c13).
% 2.86/3.00 0 [] complete_relstr($c13).
% 2.86/3.00 0 [] lower_bounded_relstr($c13).
% 2.86/3.00 0 [] upper_bounded_relstr($c13).
% 2.86/3.00 0 [] bounded_relstr($c13).
% 2.86/3.00 0 [] empty(A)|element($f15(A),powerset(A)).
% 2.86/3.00 0 [] empty(A)| -empty($f15(A)).
% 2.86/3.00 0 [] empty(A)|finite($f15(A)).
% 2.86/3.00 0 [] relation($c14).
% 2.86/3.00 0 [] relation_empty_yielding($c14).
% 2.86/3.00 0 [] one_sorted_str($c15).
% 2.86/3.00 0 [] -empty_carrier($c15).
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|element($f16(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -empty($f16(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|open_subset($f16(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|closed_subset($f16(A),A).
% 2.86/3.00 0 [] -one_sorted_str(A)|element($f17(A),powerset(powerset(the_carrier(A)))).
% 2.86/3.00 0 [] -one_sorted_str(A)| -empty($f17(A)).
% 2.86/3.00 0 [] -one_sorted_str(A)|finite($f17(A)).
% 2.86/3.00 0 [] empty(A)|element($f18(A),powerset(A)).
% 2.86/3.00 0 [] empty(A)| -empty($f18(A)).
% 2.86/3.00 0 [] empty(A)|finite($f18(A)).
% 2.86/3.00 0 [] -top_str(A)|element($f19(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] -top_str(A)|empty($f19(A)).
% 2.86/3.00 0 [] -top_str(A)|v1_membered($f19(A)).
% 2.86/3.00 0 [] -top_str(A)|v2_membered($f19(A)).
% 2.86/3.00 0 [] -top_str(A)|v3_membered($f19(A)).
% 2.86/3.00 0 [] -top_str(A)|v4_membered($f19(A)).
% 2.86/3.00 0 [] -top_str(A)|v5_membered($f19(A)).
% 2.86/3.00 0 [] -top_str(A)|boundary_set($f19(A),A).
% 2.86/3.00 0 [] rel_str($c16).
% 2.86/3.00 0 [] -empty_carrier($c16).
% 2.86/3.00 0 [] strict_rel_str($c16).
% 2.86/3.00 0 [] transitive_relstr($c16).
% 2.86/3.00 0 [] directed_relstr($c16).
% 2.86/3.00 0 [] empty_carrier(A)| -one_sorted_str(A)|element($f20(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f20(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|element($f21(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|empty($f21(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|open_subset($f21(A),A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|closed_subset($f21(A),A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|v1_membered($f21(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|v2_membered($f21(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|v3_membered($f21(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|v4_membered($f21(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|v5_membered($f21(A)).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|boundary_set($f21(A),A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|nowhere_dense($f21(A),A).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|element($f22(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] -topological_space(A)| -top_str(A)|closed_subset($f22(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|element($f23(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -empty($f23(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|closed_subset($f23(A),A).
% 2.86/3.00 0 [] -rel_str(A)|element($f24(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] -rel_str(A)|lower_relstr_subset($f24(A),A).
% 2.86/3.00 0 [] -rel_str(A)|upper_relstr_subset($f24(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -rel_str(A)|element($f25(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] empty_carrier(A)| -rel_str(A)| -empty($f25(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset($f25(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset($f25(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f26(A),powerset(the_carrier(A))).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f26(A)).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|directed_subset($f26(A),A).
% 2.86/3.00 0 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|lower_relstr_subset($f26(A),A).
% 2.86/3.00 0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 2.86/3.00 0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 2.86/3.00 0 [] subset(A,A).
% 2.86/3.00 0 [] -in(A,B)|element(A,B).
% 2.86/3.00 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.86/3.00 0 [] in($f27(A,B),A)|in($f27(A,B),B)|A=B.
% 2.86/3.00 0 [] -in($f27(A,B),A)| -in($f27(A,B),B)|A=B.
% 2.86/3.00 0 [] -element(A,powerset(B))|subset(A,B).
% 2.86/3.00 0 [] element(A,powerset(B))| -subset(A,B).
% 2.86/3.00 0 [] -empty_carrier($c19).
% 2.86/3.00 0 [] topological_space($c19).
% 2.86/3.00 0 [] top_str($c19).
% 2.86/3.00 0 [] element($c18,the_carrier($c19)).
% 2.86/3.00 0 [] in($c17,neighborhood_system($c19,$c18))|point_neighbourhood($c17,$c19,$c18).
% 2.86/3.01 0 [] -in($c17,neighborhood_system($c19,$c18))| -point_neighbourhood($c17,$c19,$c18).
% 2.86/3.01 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.86/3.01 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.86/3.01 0 [] -empty(A)|A=empty_set.
% 2.86/3.01 0 [] -in(A,B)| -empty(B).
% 2.86/3.01 0 [] -empty(A)|A=B| -empty(B).
% 2.86/3.01 end_of_list.
% 2.86/3.01
% 2.86/3.01 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=9.
% 2.86/3.01
% 2.86/3.01 This ia a non-Horn set with equality. The strategy will be
% 2.86/3.01 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.86/3.01 deletion, with positive clauses in sos and nonpositive
% 2.86/3.01 clauses in usable.
% 2.86/3.01
% 2.86/3.01 dependent: set(knuth_bendix).
% 2.86/3.01 dependent: set(anl_eq).
% 2.86/3.01 dependent: set(para_from).
% 2.86/3.01 dependent: set(para_into).
% 2.86/3.01 dependent: clear(para_from_right).
% 2.86/3.01 dependent: clear(para_into_right).
% 2.86/3.01 dependent: set(para_from_vars).
% 2.86/3.01 dependent: set(eq_units_both_ways).
% 2.86/3.01 dependent: set(dynamic_demod_all).
% 2.86/3.01 dependent: set(dynamic_demod).
% 2.86/3.01 dependent: set(order_eq).
% 2.86/3.01 dependent: set(back_demod).
% 2.86/3.01 dependent: set(lrpo).
% 2.86/3.01 dependent: set(hyper_res).
% 2.86/3.01 dependent: set(unit_deletion).
% 2.86/3.01 dependent: set(factor).
% 2.86/3.01
% 2.86/3.01 ------------> process usable:
% 2.86/3.01 ** KEPT (pick-wt=11): 2 [copy,1,flip.3] -rel_str(A)| -strict_rel_str(A)|rel_str_of(the_carrier(A),the_InternalRel(A))=A.
% 2.86/3.01 ** KEPT (pick-wt=6): 3 [] -in(A,B)| -in(B,A).
% 2.86/3.01 ** KEPT (pick-wt=10): 4 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|up_complete_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=10): 5 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -complete_relstr(A)|join_complete_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=10): 6 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -join_complete_relstr(A)|lower_bounded_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=18): 7 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|with_infima_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=18): 8 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|complete_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=18): 9 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=18): 10 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -lower_bounded_relstr(A)| -up_complete_relstr(A)|bounded_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=12): 11 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -join_complete_relstr(A)|with_infima_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=14): 12 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -antisymmetric_relstr(A)| -upper_bounded_relstr(A)| -join_complete_relstr(A)|with_suprema_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=4): 13 [] -empty(A)|finite(A).
% 2.86/3.01 ** KEPT (pick-wt=6): 14 [] -rel_str(A)| -with_suprema_relstr(A)| -empty_carrier(A).
% 2.86/3.01 ** KEPT (pick-wt=4): 15 [] -empty(A)|relation(A).
% 2.86/3.01 ** KEPT (pick-wt=8): 16 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 2.86/3.01 ** KEPT (pick-wt=14): 17 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|open_subset(B,A).
% 2.86/3.01 ** KEPT (pick-wt=14): 18 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|closed_subset(B,A).
% 2.86/3.01 ** KEPT (pick-wt=8): 19 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_suprema_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=8): 20 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|with_infima_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=8): 21 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 2.86/3.01 ** KEPT (pick-wt=6): 22 [] -rel_str(A)| -with_infima_relstr(A)| -empty_carrier(A).
% 2.86/3.01 ** KEPT (pick-wt=12): 23 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|boundary_set(B,A).
% 2.86/3.01 ** KEPT (pick-wt=10): 24 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|transitive_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=10): 25 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|antisymmetric_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=10): 26 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|complete_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=14): 27 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -empty(B)|nowhere_dense(B,A).
% 2.86/3.01 ** KEPT (pick-wt=8): 28 [] -rel_str(A)|empty_carrier(A)| -complete_relstr(A)|bounded_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=15): 29 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -nowhere_dense(B,A)|boundary_set(B,A).
% 2.86/3.01 ** KEPT (pick-wt=6): 30 [] -rel_str(A)| -bounded_relstr(A)|lower_bounded_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=6): 31 [] -rel_str(A)| -bounded_relstr(A)|upper_bounded_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=18): 32 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)| -boundary_set(B,A)|nowhere_dense(B,A).
% 2.86/3.01 ** KEPT (pick-wt=10): 33 [] -rel_str(A)|empty_carrier(A)| -reflexive_relstr(A)| -trivial_carrier(A)|connected_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=8): 34 [] -rel_str(A)| -lower_bounded_relstr(A)| -upper_bounded_relstr(A)|bounded_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=17): 35 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|empty(B).
% 2.86/3.01 ** KEPT (pick-wt=18): 36 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|closed_subset(B,A).
% 2.86/3.01 ** KEPT (pick-wt=17): 37 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v1_membered(B).
% 2.86/3.01 ** KEPT (pick-wt=17): 38 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v2_membered(B).
% 2.86/3.01 ** KEPT (pick-wt=17): 39 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v3_membered(B).
% 2.86/3.01 ** KEPT (pick-wt=17): 40 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v4_membered(B).
% 2.86/3.01 ** KEPT (pick-wt=17): 41 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|v5_membered(B).
% 2.86/3.01 Following clause subsumed by 29 during input processing: 0 [] -topological_space(A)| -top_str(A)| -element(B,powerset(the_carrier(A)))| -open_subset(B,A)| -nowhere_dense(B,A)|boundary_set(B,A).
% 2.86/3.01 Following clause subsumed by 14 during input processing: 0 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)| -empty_carrier(A).
% 2.86/3.01 ** KEPT (pick-wt=10): 42 [] -rel_str(A)| -reflexive_relstr(A)| -with_suprema_relstr(A)| -up_complete_relstr(A)|upper_bounded_relstr(A).
% 2.86/3.01 ** KEPT (pick-wt=17): 43 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))|neighborhood_system(A,B)=a_2_0_yellow19(A,B).
% 2.86/3.01 ** KEPT (pick-wt=8): 44 [] -relation_of2(A,B,B)|strict_rel_str(rel_str_of(B,A)).
% 2.86/3.01 ** KEPT (pick-wt=8): 45 [] -relation_of2(A,B,B)|rel_str(rel_str_of(B,A)).
% 2.86/3.01 ** KEPT (pick-wt=19): 46 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))|element(neighborhood_system(A,B),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(A))))).
% 2.86/3.01 ** KEPT (pick-wt=8): 47 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=4): 48 [] -rel_str(A)|one_sorted_str(A).
% 2.86/3.01 ** KEPT (pick-wt=4): 49 [] -top_str(A)|one_sorted_str(A).
% 2.86/3.01 ** KEPT (pick-wt=19): 50 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -point_neighbourhood(C,A,B)|element(C,powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=10): 51 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 2.86/3.01 ** KEPT (pick-wt=9): 52 [] -rel_str(A)|relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)).
% 2.86/3.01 ** KEPT (pick-wt=16): 53 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))|point_neighbourhood($f1(A,B),A,B).
% 2.86/3.01 ** KEPT (pick-wt=8): 54 [] -finite(A)| -finite(B)|finite(cartesian_product2(A,B)).
% 2.86/3.01 ** KEPT (pick-wt=7): 55 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.01 ** KEPT (pick-wt=8): 56 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset(cast_as_carrier_subset(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 57 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset(cast_as_carrier_subset(A),A).
% 2.86/3.01 ** KEPT (pick-wt=7): 58 [] empty_carrier(A)| -one_sorted_str(A)| -empty(the_carrier(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 59 [] -empty(powerset(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 60 [] -empty_carrier(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 61 [] -v1_yellow_3(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=7): 62 [] empty_carrier(A)| -one_sorted_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.01 ** KEPT (pick-wt=7): 63 [] -with_suprema_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.01 ** KEPT (pick-wt=8): 64 [] -with_suprema_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 2.86/3.01 Following clause subsumed by 60 during input processing: 0 [] empty(A)| -empty_carrier(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=5): 65 [] empty(A)| -trivial_carrier(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 61 during input processing: 0 [] empty(A)| -v1_yellow_3(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 55 during input processing: 0 [] empty_carrier(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.01 Following clause subsumed by 55 during input processing: 0 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.01 ** KEPT (pick-wt=10): 66 [] empty_carrier(A)| -upper_bounded_relstr(A)| -rel_str(A)|directed_subset(cast_as_carrier_subset(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 67 [] empty(A)|empty(B)| -empty(cartesian_product2(A,B)).
% 2.86/3.01 ** KEPT (pick-wt=7): 68 [] -with_infima_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.01 ** KEPT (pick-wt=8): 69 [] -with_infima_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 70 [] -topological_space(A)| -top_str(A)|closed_subset(cast_as_carrier_subset(A),A).
% 2.86/3.01 Following clause subsumed by 55 during input processing: 0 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)| -empty(cast_as_carrier_subset(A)).
% 2.86/3.01 ** KEPT (pick-wt=10): 71 [] empty_carrier(A)| -lower_bounded_relstr(A)| -rel_str(A)|filtered_subset(cast_as_carrier_subset(A),A).
% 2.86/3.01 Following clause subsumed by 60 during input processing: 0 [] -empty_carrier(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=8): 72 [] -topological_space(A)| -top_str(A)|open_subset(cast_as_carrier_subset(A),A).
% 2.86/3.01 Following clause subsumed by 70 during input processing: 0 [] -topological_space(A)| -top_str(A)|closed_subset(cast_as_carrier_subset(A),A).
% 2.86/3.01 Following clause subsumed by 60 during input processing: 0 [] -empty_carrier(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 60 during input processing: 0 [] -empty_carrier(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 61 during input processing: 0 [] -v1_yellow_3(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=6): 73 [] -top_str(A)|dense(cast_as_carrier_subset(A),A).
% 2.86/3.01 ** KEPT (pick-wt=22): 74 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -in(C,a_2_0_yellow19(A,B))|point_neighbourhood($f5(C,A,B),A,B).
% 2.86/3.01 ** KEPT (pick-wt=21): 76 [copy,75,flip.6] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))| -in(C,a_2_0_yellow19(A,B))|$f5(C,A,B)=C.
% 2.86/3.01 ** KEPT (pick-wt=22): 77 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -element(B,the_carrier(A))|in(C,a_2_0_yellow19(A,B))| -point_neighbourhood(D,A,B)|C!=D.
% 2.86/3.01 ** KEPT (pick-wt=14): 78 [] -relation_of2(A,B,B)|rel_str_of(B,A)!=rel_str_of(C,D)|B=C.
% 2.86/3.01 ** KEPT (pick-wt=14): 79 [] -relation_of2(A,B,B)|rel_str_of(B,A)!=rel_str_of(C,D)|A=D.
% 2.86/3.01 ** KEPT (pick-wt=14): 80 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f6(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=11): 81 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f6(A)).
% 2.86/3.01 ** KEPT (pick-wt=12): 82 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|filtered_subset($f6(A),A).
% 2.86/3.01 ** KEPT (pick-wt=12): 83 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|upper_relstr_subset($f6(A),A).
% 2.86/3.01 ** KEPT (pick-wt=18): 84 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|element($f7(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=15): 85 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)| -empty($f7(A)).
% 2.86/3.01 ** KEPT (pick-wt=16): 86 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|directed_subset($f7(A),A).
% 2.86/3.01 ** KEPT (pick-wt=16): 87 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|filtered_subset($f7(A),A).
% 2.86/3.01 ** KEPT (pick-wt=16): 88 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|lower_relstr_subset($f7(A),A).
% 2.86/3.01 ** KEPT (pick-wt=16): 89 [] -reflexive_relstr(A)| -transitive_relstr(A)| -antisymmetric_relstr(A)| -with_suprema_relstr(A)| -with_infima_relstr(A)| -rel_str(A)|upper_relstr_subset($f7(A),A).
% 2.86/3.01 ** KEPT (pick-wt=2): 90 [] -empty_carrier($c4).
% 2.86/3.01 ** KEPT (pick-wt=2): 91 [] -empty_carrier($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 92 [] -empty($c6).
% 2.86/3.01 ** KEPT (pick-wt=2): 93 [] -empty_carrier($c7).
% 2.86/3.01 ** KEPT (pick-wt=5): 94 [] empty(A)| -empty($f8(A)).
% 2.86/3.01 ** KEPT (pick-wt=10): 95 [] -topological_space(A)| -top_str(A)|element($f9(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=8): 96 [] -topological_space(A)| -top_str(A)|open_subset($f9(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 97 [] -rel_str(A)|element($f10(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=6): 98 [] -rel_str(A)|directed_subset($f10(A),A).
% 2.86/3.01 ** KEPT (pick-wt=6): 99 [] -rel_str(A)|filtered_subset($f10(A),A).
% 2.86/3.01 ** KEPT (pick-wt=2): 100 [] -empty_carrier($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 101 [] -trivial_carrier($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 102 [] -v1_yellow_3($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 103 [] -empty_carrier($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 104 [] -empty_carrier($c11).
% 2.86/3.01 ** KEPT (pick-wt=2): 105 [] -empty($c12).
% 2.86/3.01 ** KEPT (pick-wt=10): 106 [] -topological_space(A)| -top_str(A)|element($f12(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=8): 107 [] -topological_space(A)| -top_str(A)|open_subset($f12(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 108 [] -topological_space(A)| -top_str(A)|closed_subset($f12(A),A).
% 2.86/3.01 ** KEPT (pick-wt=12): 109 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|element($f13(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=9): 110 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)| -empty($f13(A)).
% 2.86/3.01 ** KEPT (pick-wt=9): 111 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|finite($f13(A)).
% 2.86/3.01 ** KEPT (pick-wt=10): 112 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|directed_subset($f13(A),A).
% 2.86/3.01 ** KEPT (pick-wt=10): 113 [] empty_carrier(A)| -reflexive_relstr(A)| -rel_str(A)|filtered_subset($f13(A),A).
% 2.86/3.01 ** KEPT (pick-wt=3): 114 [] -empty($f14(A)).
% 2.86/3.01 ** KEPT (pick-wt=2): 115 [] -empty_carrier($c13).
% 2.86/3.01 ** KEPT (pick-wt=5): 116 [] empty(A)| -empty($f15(A)).
% 2.86/3.01 ** KEPT (pick-wt=2): 117 [] -empty_carrier($c15).
% 2.86/3.01 ** KEPT (pick-wt=12): 118 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|element($f16(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=9): 119 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -empty($f16(A)).
% 2.86/3.01 ** KEPT (pick-wt=10): 120 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|open_subset($f16(A),A).
% 2.86/3.01 ** KEPT (pick-wt=10): 121 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|closed_subset($f16(A),A).
% 2.86/3.01 ** KEPT (pick-wt=9): 122 [] -one_sorted_str(A)|element($f17(A),powerset(powerset(the_carrier(A)))).
% 2.86/3.01 ** KEPT (pick-wt=5): 123 [] -one_sorted_str(A)| -empty($f17(A)).
% 2.86/3.01 ** KEPT (pick-wt=5): 124 [] -one_sorted_str(A)|finite($f17(A)).
% 2.86/3.01 ** KEPT (pick-wt=5): 125 [] empty(A)| -empty($f18(A)).
% 2.86/3.01 ** KEPT (pick-wt=8): 126 [] -top_str(A)|element($f19(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=5): 127 [] -top_str(A)|empty($f19(A)).
% 2.86/3.01 ** KEPT (pick-wt=5): 128 [] -top_str(A)|v1_membered($f19(A)).
% 2.86/3.01 ** KEPT (pick-wt=5): 129 [] -top_str(A)|v2_membered($f19(A)).
% 2.86/3.01 ** KEPT (pick-wt=5): 130 [] -top_str(A)|v3_membered($f19(A)).
% 2.86/3.01 ** KEPT (pick-wt=5): 131 [] -top_str(A)|v4_membered($f19(A)).
% 2.86/3.01 ** KEPT (pick-wt=5): 132 [] -top_str(A)|v5_membered($f19(A)).
% 2.86/3.01 ** KEPT (pick-wt=6): 133 [] -top_str(A)|boundary_set($f19(A),A).
% 2.86/3.01 ** KEPT (pick-wt=2): 134 [] -empty_carrier($c16).
% 2.86/3.01 ** KEPT (pick-wt=10): 135 [] empty_carrier(A)| -one_sorted_str(A)|element($f20(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=7): 136 [] empty_carrier(A)| -one_sorted_str(A)| -empty($f20(A)).
% 2.86/3.01 ** KEPT (pick-wt=10): 137 [] -topological_space(A)| -top_str(A)|element($f21(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=7): 138 [] -topological_space(A)| -top_str(A)|empty($f21(A)).
% 2.86/3.01 ** KEPT (pick-wt=8): 139 [] -topological_space(A)| -top_str(A)|open_subset($f21(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 140 [] -topological_space(A)| -top_str(A)|closed_subset($f21(A),A).
% 2.86/3.01 ** KEPT (pick-wt=7): 141 [] -topological_space(A)| -top_str(A)|v1_membered($f21(A)).
% 2.86/3.01 ** KEPT (pick-wt=7): 142 [] -topological_space(A)| -top_str(A)|v2_membered($f21(A)).
% 2.86/3.01 ** KEPT (pick-wt=7): 143 [] -topological_space(A)| -top_str(A)|v3_membered($f21(A)).
% 2.86/3.01 ** KEPT (pick-wt=7): 144 [] -topological_space(A)| -top_str(A)|v4_membered($f21(A)).
% 2.86/3.01 ** KEPT (pick-wt=7): 145 [] -topological_space(A)| -top_str(A)|v5_membered($f21(A)).
% 2.86/3.01 ** KEPT (pick-wt=8): 146 [] -topological_space(A)| -top_str(A)|boundary_set($f21(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 147 [] -topological_space(A)| -top_str(A)|nowhere_dense($f21(A),A).
% 2.86/3.01 ** KEPT (pick-wt=10): 148 [] -topological_space(A)| -top_str(A)|element($f22(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=8): 149 [] -topological_space(A)| -top_str(A)|closed_subset($f22(A),A).
% 2.86/3.01 ** KEPT (pick-wt=12): 150 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|element($f23(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=9): 151 [] empty_carrier(A)| -topological_space(A)| -top_str(A)| -empty($f23(A)).
% 2.86/3.01 ** KEPT (pick-wt=10): 152 [] empty_carrier(A)| -topological_space(A)| -top_str(A)|closed_subset($f23(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 153 [] -rel_str(A)|element($f24(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=6): 154 [] -rel_str(A)|lower_relstr_subset($f24(A),A).
% 2.86/3.01 ** KEPT (pick-wt=6): 155 [] -rel_str(A)|upper_relstr_subset($f24(A),A).
% 2.86/3.01 ** KEPT (pick-wt=10): 156 [] empty_carrier(A)| -rel_str(A)|element($f25(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=7): 157 [] empty_carrier(A)| -rel_str(A)| -empty($f25(A)).
% 2.86/3.01 ** KEPT (pick-wt=8): 158 [] empty_carrier(A)| -rel_str(A)|lower_relstr_subset($f25(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 159 [] empty_carrier(A)| -rel_str(A)|upper_relstr_subset($f25(A),A).
% 2.86/3.01 ** KEPT (pick-wt=14): 160 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|element($f26(A),powerset(the_carrier(A))).
% 2.86/3.01 ** KEPT (pick-wt=11): 161 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)| -empty($f26(A)).
% 2.86/3.01 ** KEPT (pick-wt=12): 162 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|directed_subset($f26(A),A).
% 2.86/3.01 ** KEPT (pick-wt=12): 163 [] empty_carrier(A)| -reflexive_relstr(A)| -transitive_relstr(A)| -rel_str(A)|lower_relstr_subset($f26(A),A).
% 2.86/3.01 ** KEPT (pick-wt=8): 164 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 2.86/3.01 ** KEPT (pick-wt=8): 165 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 2.86/3.01 ** KEPT (pick-wt=6): 166 [] -in(A,B)|element(A,B).
% 2.86/3.01 ** KEPT (pick-wt=8): 167 [] -element(A,B)|empty(B)|in(A,B).
% 2.86/3.01 ** KEPT (pick-wt=13): 168 [] -in($f27(A,B),A)| -in($f27(A,B),B)|A=B.
% 2.86/3.01 ** KEPT (pick-wt=7): 169 [] -element(A,powerset(B))|subset(A,B).
% 2.86/3.01 ** KEPT (pick-wt=7): 170 [] element(A,powerset(B))| -subset(A,B).
% 2.86/3.01 ** KEPT (pick-wt=2): 171 [] -empty_carrier($c19).
% 2.86/3.01 ** KEPT (pick-wt=9): 172 [] -in($c17,neighborhood_system($c19,$c18))| -point_neighbourhood($c17,$c19,$c18).
% 2.86/3.01 ** KEPT (pick-wt=10): 173 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 2.86/3.01 ** KEPT (pick-wt=9): 174 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 2.86/3.01 ** KEPT (pick-wt=5): 175 [] -empty(A)|A=empty_set.
% 2.86/3.01 ** KEPT (pick-wt=5): 176 [] -in(A,B)| -empty(B).
% 2.86/3.01 ** KEPT (pick-wt=7): 177 [] -empty(A)|A=B| -empty(B).
% 2.86/3.01 42 back subsumes 9.
% 2.86/3.01
% 2.86/3.01 ------------> process sos:
% 2.86/3.01 ** KEPT (pick-wt=3): 183 [] A=A.
% 2.86/3.01 ** KEPT (pick-wt=3): 184 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 185 [] rel_str(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=2): 186 [] rel_str($c1).
% 2.86/3.01 ** KEPT (pick-wt=2): 187 [] top_str($c2).
% 2.86/3.01 ** KEPT (pick-wt=2): 188 [] one_sorted_str($c3).
% 2.86/3.01 ** KEPT (pick-wt=6): 189 [] relation_of2($f2(A,B),A,B).
% 2.86/3.01 ** KEPT (pick-wt=4): 190 [] element($f3(A),A).
% 2.86/3.01 ** KEPT (pick-wt=6): 191 [] relation_of2_as_subset($f4(A,B),A,B).
% 2.86/3.01 ** KEPT (pick-wt=2): 192 [] empty(empty_set).
% 2.86/3.01 ** KEPT (pick-wt=2): 193 [] relation(empty_set).
% 2.86/3.01 ** KEPT (pick-wt=2): 194 [] relation_empty_yielding(empty_set).
% 2.86/3.01 Following clause subsumed by 184 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 195 [] reflexive_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 196 [] transitive_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 197 [] antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 198 [] lower_bounded_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 199 [] upper_bounded_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 200 [] bounded_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 201 [] up_complete_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 202 [] join_complete_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 203 [] distributive_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 204 [] heyting_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 205 [] complemented_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 206 [] boolean_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 207 [] with_suprema_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 208 [] with_infima_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 209 [] complete_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 184 during input processing: 0 [] empty(A)|strict_rel_str(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 195 during input processing: 0 [] empty(A)|reflexive_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 196 during input processing: 0 [] empty(A)|transitive_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 197 during input processing: 0 [] empty(A)|antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 198 during input processing: 0 [] empty(A)|lower_bounded_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 199 during input processing: 0 [] empty(A)|upper_bounded_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 200 during input processing: 0 [] empty(A)|bounded_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 201 during input processing: 0 [] empty(A)|up_complete_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 202 during input processing: 0 [] empty(A)|join_complete_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 203 during input processing: 0 [] empty(A)|distributive_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 204 during input processing: 0 [] empty(A)|heyting_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 205 during input processing: 0 [] empty(A)|complemented_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 206 during input processing: 0 [] empty(A)|boolean_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 207 during input processing: 0 [] empty(A)|with_suprema_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 208 during input processing: 0 [] empty(A)|with_infima_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 209 during input processing: 0 [] empty(A)|complete_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 192 during input processing: 0 [] empty(empty_set).
% 2.86/3.01 Following clause subsumed by 193 during input processing: 0 [] relation(empty_set).
% 2.86/3.01 Following clause subsumed by 184 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 195 during input processing: 0 [] reflexive_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 196 during input processing: 0 [] transitive_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 197 during input processing: 0 [] antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 184 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 195 during input processing: 0 [] reflexive_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 196 during input processing: 0 [] transitive_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 197 during input processing: 0 [] antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 198 during input processing: 0 [] lower_bounded_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 199 during input processing: 0 [] upper_bounded_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 200 during input processing: 0 [] bounded_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 207 during input processing: 0 [] with_suprema_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 208 during input processing: 0 [] with_infima_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 209 during input processing: 0 [] complete_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 184 during input processing: 0 [] strict_rel_str(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 195 during input processing: 0 [] reflexive_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 196 during input processing: 0 [] transitive_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 197 during input processing: 0 [] antisymmetric_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 198 during input processing: 0 [] lower_bounded_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 199 during input processing: 0 [] upper_bounded_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 200 during input processing: 0 [] bounded_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 210 [] directed_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 201 during input processing: 0 [] up_complete_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 202 during input processing: 0 [] join_complete_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 207 during input processing: 0 [] with_suprema_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 208 during input processing: 0 [] with_infima_relstr(boole_POSet(A)).
% 2.86/3.01 Following clause subsumed by 209 during input processing: 0 [] complete_relstr(boole_POSet(A)).
% 2.86/3.01 ** KEPT (pick-wt=2): 211 [] rel_str($c4).
% 2.86/3.01 ** KEPT (pick-wt=2): 212 [] reflexive_relstr($c4).
% 2.86/3.01 ** KEPT (pick-wt=2): 213 [] transitive_relstr($c4).
% 2.86/3.01 ** KEPT (pick-wt=2): 214 [] antisymmetric_relstr($c4).
% 2.86/3.01 ** KEPT (pick-wt=2): 215 [] connected_relstr($c4).
% 2.86/3.01 ** KEPT (pick-wt=2): 216 [] rel_str($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 217 [] strict_rel_str($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 218 [] reflexive_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 219 [] transitive_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 220 [] antisymmetric_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 221 [] with_suprema_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 222 [] with_infima_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 223 [] complete_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 224 [] lower_bounded_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 225 [] upper_bounded_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 226 [] bounded_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 227 [] up_complete_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 228 [] join_complete_relstr($c5).
% 2.86/3.01 ** KEPT (pick-wt=2): 229 [] finite($c6).
% 2.86/3.01 ** KEPT (pick-wt=2): 230 [] rel_str($c7).
% 2.86/3.01 ** KEPT (pick-wt=2): 231 [] strict_rel_str($c7).
% 2.86/3.01 ** KEPT (pick-wt=2): 232 [] reflexive_relstr($c7).
% 2.86/3.01 ** KEPT (pick-wt=2): 233 [] transitive_relstr($c7).
% 2.86/3.01 ** KEPT (pick-wt=2): 234 [] antisymmetric_relstr($c7).
% 2.86/3.01 ** KEPT (pick-wt=2): 235 [] complete_relstr($c7).
% 2.86/3.01 ** KEPT (pick-wt=2): 236 [] empty($c8).
% 2.86/3.01 ** KEPT (pick-wt=2): 237 [] relation($c8).
% 2.86/3.01 ** KEPT (pick-wt=7): 238 [] empty(A)|element($f8(A),powerset(A)).
% 2.86/3.01 ** KEPT (pick-wt=2): 239 [] rel_str($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 240 [] strict_rel_str($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 241 [] reflexive_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 242 [] transitive_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 243 [] antisymmetric_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 244 [] lower_bounded_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 245 [] upper_bounded_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 246 [] bounded_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 247 [] distributive_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 248 [] heyting_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 249 [] complemented_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 250 [] boolean_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 251 [] with_suprema_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 252 [] with_infima_relstr($c9).
% 2.86/3.01 ** KEPT (pick-wt=2): 253 [] rel_str($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 254 [] strict_rel_str($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 255 [] reflexive_relstr($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 256 [] transitive_relstr($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 257 [] antisymmetric_relstr($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 258 [] with_suprema_relstr($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 259 [] with_infima_relstr($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 260 [] complete_relstr($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 261 [] trivial_carrier($c10).
% 2.86/3.01 ** KEPT (pick-wt=2): 262 [] rel_str($c11).
% 2.86/3.01 ** KEPT (pick-wt=2): 263 [] strict_rel_str($c11).
% 2.86/3.01 ** KEPT (pick-wt=2): 264 [] reflexive_relstr($c11).
% 2.86/3.01 ** KEPT (pick-wt=2): 265 [] transitive_relstr($c11).
% 2.86/3.01 ** KEPT (pick-wt=2): 266 [] antisymmetric_relstr($c11).
% 2.86/3.01 ** KEPT (pick-wt=2): 267 [] with_suprema_relstr($c11).
% 2.86/3.01 ** KEPT (pick-wt=2): 268 [] with_infima_relstr($c11).
% 2.86/3.01 ** KEPT (pick-wt=2): 269 [] complete_relstr($c11).
% 2.86/3.01 ** KEPT (pick-wt=2): 270 [] relation($c12).
% 2.86/3.01 ** KEPT (pick-wt=5): 271 [] element($f11(A),powerset(A)).
% 2.86/3.01 ** KEPT (pick-wt=3): 272 [] empty($f11(A)).
% 2.86/3.01 ** KEPT (pick-wt=6): 273 [] element($f14(A),powerset(powerset(A))).
% 2.86/3.01 ** KEPT (pick-wt=3): 274 [] finite($f14(A)).
% 2.86/3.01 ** KEPT (pick-wt=2): 275 [] rel_str($c13).
% 2.86/3.01 ** KEPT (pick-wt=2): 276 [] reflexive_relstr($c13).
% 2.86/3.01 ** KEPT (pick-wt=2): 277 [] transitive_relstr($c13).
% 2.86/3.01 ** KEPT (pick-wt=2): 278 [] antisymmetric_relstr($c13).
% 2.86/3.01 ** KEPT (pick-wt=2): 279 [] with_suprema_relstr($c13).
% 2.86/3.01 ** KEPT (pick-wt=2): 280 [] with_infima_relstr($c13).
% 2.86/3.01 ** KEPT (pick-wt=2): 281 [] complete_relstr($c13).
% 2.86/3.01 ** KEPT (pick-wt=2): 282 [] lower_bounded_relstr($c13).
% 2.86/3.01 ** KEPT (pick-wt=2): 283 [] upper_bounded_relstr($c13).
% 2.86/3.01 ** KEPT (pick-wt=2): 284 [] bounded_relstr($c13).
% 2.86/3.01 ** KEPT (pick-wt=7): 285 [] empty(A)|element($f15(A),powerset(A)).
% 2.86/3.01 ** KEPT (pick-wt=5): 286 [] empty(A)|finite($f15(A)).
% 2.86/3.01 ** KEPT (pick-wt=2): 287 [] relation($c14).
% 2.86/3.01 ** KEPT (pick-wt=2): 288 [] relation_empty_yielding($c14).
% 3.01/3.18 ** KEPT (pick-wt=2): 289 [] one_sorted_str($c15).
% 3.01/3.18 ** KEPT (pick-wt=7): 290 [] empty(A)|element($f18(A),powerset(A)).
% 3.01/3.18 ** KEPT (pick-wt=5): 291 [] empty(A)|finite($f18(A)).
% 3.01/3.18 ** KEPT (pick-wt=2): 292 [] rel_str($c16).
% 3.01/3.18 ** KEPT (pick-wt=2): 293 [] strict_rel_str($c16).
% 3.01/3.18 ** KEPT (pick-wt=2): 294 [] transitive_relstr($c16).
% 3.01/3.18 ** KEPT (pick-wt=2): 295 [] directed_relstr($c16).
% 3.01/3.18 ** KEPT (pick-wt=3): 296 [] subset(A,A).
% 3.01/3.18 ** KEPT (pick-wt=13): 297 [] in($f27(A,B),A)|in($f27(A,B),B)|A=B.
% 3.01/3.18 ** KEPT (pick-wt=2): 298 [] topological_space($c19).
% 3.01/3.18 ** KEPT (pick-wt=2): 299 [] top_str($c19).
% 3.01/3.18 ** KEPT (pick-wt=4): 300 [] element($c18,the_carrier($c19)).
% 3.01/3.18 ** KEPT (pick-wt=9): 301 [] in($c17,neighborhood_system($c19,$c18))|point_neighbourhood($c17,$c19,$c18).
% 3.01/3.18 Following clause subsumed by 183 during input processing: 0 [copy,183,flip.1] A=A.
% 3.01/3.18 183 back subsumes 182.
% 3.01/3.18 183 back subsumes 181.
% 3.01/3.18
% 3.01/3.18 ======= end of input processing =======
% 3.01/3.18
% 3.01/3.18 =========== start of search ===========
% 3.01/3.18
% 3.01/3.18
% 3.01/3.18 Resetting weight limit to 2.
% 3.01/3.18
% 3.01/3.18
% 3.01/3.18 Resetting weight limit to 2.
% 3.01/3.18
% 3.01/3.18 sos_size=582
% 3.01/3.18
% 3.01/3.18 Search stopped because sos empty.
% 3.01/3.18
% 3.01/3.18
% 3.01/3.18 Search stopped because sos empty.
% 3.01/3.18
% 3.01/3.18 ============ end of search ============
% 3.01/3.18
% 3.01/3.18 -------------- statistics -------------
% 3.01/3.18 clauses given 674
% 3.01/3.18 clauses generated 16394
% 3.01/3.18 clauses kept 898
% 3.01/3.18 clauses forward subsumed 421
% 3.01/3.18 clauses back subsumed 3
% 3.01/3.18 Kbytes malloced 5859
% 3.01/3.18
% 3.01/3.18 ----------- times (seconds) -----------
% 3.01/3.18 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 3.01/3.18 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 3.01/3.18 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.01/3.18
% 3.01/3.18 Process 26368 finished Wed Jul 27 08:03:53 2022
% 3.01/3.18 Otter interrupted
% 3.01/3.18 PROOF NOT FOUND
%------------------------------------------------------------------------------